st: Question on aweights

Dear all,
I have a question regarding the aweights.
I am using a dataset that has data at firm level for a number of countries.
I would like to run some regressions using firm-level data but
assigning more weight to those firms that come from countries where
fewer firms were surveyed so that all the countries are equally
represented in the regression. In my sample I have African countries
with only 70 firms surveyed and countries like China with over 1500
firms surveyed. I do not want the results to represent only those
countries with a large number of observations.
I found that aweights could be useful for this. More specifically, I
can use the inverse of the number of firms surveyed in each country as
aweights and the results are going to be similar to those obtained
taking the average by country and then running the regression without
aweights. That is,
doing:
reg y x [aweight=1/nr_firms]
shows the same coefficients as doing this:
collapse (mean) y x nr_firms, by(country)
and then,
reg y x
where: y is the dependent variable, x is the independent variable,
nr_firms is the number of firms surveyed in each country, country is a
string with the name of each country.
I have run these two regressions and the coefficients are exactly the
same, but the Standard Errors differ. In fact, in the regression using
the firm-level data and aweights the variable x is significant at 1
percent, while in the regression of the country averages the same
variable is not significant.
Obviously, the difference is in the Mean of Square Errors. Why are
they that different? I understand that they can be different, but why
is there such a big difference in the significance levels. Is anything
wrong? Should I change the the SE when I am working with aweights?
These are the results of both regressions:
Using firm level data and aweights
(sum of wgt is 6.1000e+01)
Source | SS df MS
Number of obs = 44244
-------------+--------------------------------------------------------------
F( 1, 44242) = 118.27
Model | 26.1492442 1 26.1492442
Prob > F = 0.0000
Residual | 9781.57782 44242 .221092578
R-squared = 0.0027
-------------+--------------------------------------------------------------
Adj R-squared = 0.0026
Total | 9807.72706 44243 .221678617 Root
MSE = .4702
--------------------------------------------------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t|
[95% Conf. Interval]
-------------+-----------------------------------------------------------------------------------------------------------
x | .1231604 .0113248 10.88 0.000
.1009637 .1453572
_cons | .5841591 .0080537 72.53 0.000 .5683737
.5999445
---------------------------------------------------------------------------------------------------------------------------
Using country averages and no weights
Source | SS df MS
Number of obs = 61
-------------+--------------------------------------------------
F( 1, 59) = 0.88
Model | .036052432 1 .036052432 Prob > F
= 0.3524
Residual | 2.42089584 59 .041032133 R-squared = 0.0147
-------------+--------------------------------------------------
Adj R-squared = -0.0020
Total | 2.45694827 60 .040949138 Root MSE
= .20256
---------------------------------------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95%
Conf. Interval]
-------------+-----------------------------------------------------------------------------------------------
x | .1231604 .1313911 0.94 0.352
-.1397526 .3860734
_cons | .5841591 .0934402 6.25 0.000 .3971856 .7711326
-------------------------------------------------------------------------------------------------------------------
Diego
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